grandes-ecoles 2024 Q6

grandes-ecoles · France · polytechnique-maths-a__mp Sequences and Series Evaluation of a Finite or Infinite Sum
Show that for any non-zero natural integer $n$, $$D_{n} = n! \sum_{k=0}^{n} \frac{(-1)^{k}}{k!}$$
Show that for any non-zero natural integer $n$,
$$D_{n} = n! \sum_{k=0}^{n} \frac{(-1)^{k}}{k!}$$